Buckman's first law of covariation - a case of proportionality

摘要

Buckman's first law of covariation states that in ammonoids, coarseness of ribs and other ornamentation correlates negatively with degree of compression (whorl height/width ratio) and involution. This 'law' has escaped several attempts at functional or physiological explanation. However, Buckman's first law becomes self-evident, and almost collapses to a tautology, when we reword it as follows: Size of lateral and ventral ornamentation correlates with size of the aperture (its width and height, respectively). In a shell that is strongly compressed laterally, the diameter of the aperture, and hence the soft parts within, is small in the lateral direction. For such a shell, coarse lateral ribbing would imply impossibly strong relative compression and expansion of the soft body through the formation of a rib. Conversely, if the shell is depressed (compressed dorsoventrally), the diameter of the soft parts is small in the dorsoventral direction, and the ventral ribbing correspondingly small. Buckman's first law is thus simply a statement of proportionality that needs no special explanation. On the contrary, any departure from this 'law' would imply strong deformations of the soft body as ornamentation was formed. Measurements on the Triassic ammonite Pseudodanubites halli show that ventral ribs get relatively stronger on compressed specimens, in accordance with this view of Buckman's law.